Fractional ratios and common units

Make ratio units alike

1/2:3/4 = 2:3, multiplying both terms by 4. Similarly 0.8:1.2 = 2:3. A ratio may begin with fractions or decimals, but equivalent terms use a common multiplier. For 2 m : 50 cm, first use one unit: 200 : 50 = 4 : 1.

Several terms use one common multiplier

1/2:3/4:5/4 becomes 2:3:5 when every term is multiplied by 4. For a total of 40 units shared in this ratio, ten ratio units represent 40, so the shares are 8, 12 and 20. Check the total and all corresponding ratios.

Check your understanding 1 Make the measurement units match

Simplify 0.6 m : 45 cm, then simplify 2/3:5/6.

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Use 60 cm : 45 cm = 4:3. Multiply both fractional terms by 6 to get 4:5. Converting only one ratio term by an unrelated multiplier would change the relationship.

A ratio does not specify a total

The ratio 2:3 could describe 2 and 3 objects, 20 and 30, or many other pairs. A known part, total or difference is needed to determine the actual amounts. Identify what the given quantity represents before dividing by ratio units.